Lithographic method and apparatus

Abstract

A method of correcting an optical image formed by an optical system, the method including obtaining a map indicative of a polarization dependent property of the optical system across a pupil plane of the optical system for each spatial position in an image plane of the optical system, combining the map indicative of the polarization dependent property of the optical system with a radiation map of the intensity and polarization of an input radiation beam to form an image map, and using the image map to correct an optical image formed by directing the input radiation beam through the optical system.

The invention claimed is: 
     
       1. A lithographic apparatus comprising:
 a support configured to hold a substrate; 
 a projection system configured to project a patterned radiation beam onto a target portion of the substrate to form an image thereon; and 
 an image correction system configured to:
 determine a retardation map of the image formed on the substrate; 
 determine an aberration map of the image formed on the substrate; 
 combine the retardation and aberration maps into a lithographic target map; and 
 correct, based on the lithographic target map, subsequent ones of the image formed on the substrate. 
 
 
     
     
       2. The lithographic apparatus of  claim 1 , wherein the image correction system is further configured to adjust the position of one or more optical elements of the projection system. 
     
     
       3. The lithographic apparatus of  claim 2 , wherein the image correction system is further configured to use a dynamic optical element model to calculate how to adjust the position of the one or more optical elements of the projection system. 
     
     
       4. The lithographic apparatus of  claim 1 , wherein the image correction system is further configured to translate the retardation map into a second aberration map. 
     
     
       5. The lithographic apparatus of  claim 4 , wherein the image correction system is further configured to translate the retardation map into a second aberration map by transforming one or more orientation Zernike polynomials into corresponding one or more Zernike polynomials. 
     
     
       6. The lithographic apparatus of  claim 1 , wherein the image correction system is further configured to convert the retardation map and the aberration map into one or more lithographic parameters. 
     
     
       7. The lithographic apparatus of  claim 6 , wherein the one or more lithographic parameters include at least one of displacement and defocus. 
     
     
       8. A method of correcting an optical image formed by an optical system when a radiation beam is directed through the optical system, the method comprising:
 determining a retardation map of the optical image formed by the optical system; 
 determining an aberration map of the optical image formed by the optical system; 
 combining the retardation and aberration maps into a target map; and 
 correcting, based on the target map, the optical image. 
 
     
     
       9. The method of  claim 8 , further comprising imparting a pattern to the radiation beam by a patterning device before the radiation beam enters the optical system, wherein the retardation map has information relating to the pattern. 
     
     
       10. The method of  claim 8 , wherein the correcting of the optical image comprises manipulating an optical element of the optical system. 
     
     
       11. The method of  claim 10 , further comprising using a dynamic optical element model to calculate how to manipulate the optical element of the projection system. 
     
     
       12. The method of  claim 8 , further comprising translating the retardation map into a second aberration map. 
     
     
       13. The method of  claim 12 , wherein the translating comprises transforming one or more orientation Zernike polynomials into corresponding one or more Zernike polynomials. 
     
     
       14. The method of  claim 8 , wherein the optical system is a projection system of a lithographic apparatus. 
     
     
       15. A non-transitory computer-readable storage device having instructions stored thereon, execution of which, by one or more processors, cause the one or more processors to perform operations comprising:
 projecting, by a projection system, a patterned radiation beam onto a target portion of a substrate to form an image thereon; and
 determining a retardation map of the image formed on the substrate; 
 determining an aberration map of the image formed on the substrate; 
 combining the retardation and aberration maps into a lithographic target map; and 
 correcting, based on the lithographic target map, subsequent ones of the image formed on the substrate. 
 
 
     
     
       16. The non-transitory computer-readable storage device of  claim 15 , wherein the processor is further configured to use a dynamic optical element model to calculate an adjustment to a position of an optical element of the projection system. 
     
     
       17. The non-transitory computer-readable storage device of  claim 15 , wherein the processor is further configured to translate the retardation map into a second aberration map. 
     
     
       18. The non-transitory computer-readable storage device of  claim 17 , wherein the processor is further configured to translate the retardation map into a second aberration map by transforming one or more orientation Zernike polynomials into corresponding one or more Zernike polynomials. 
     
     
       19. The non-transitory computer-readable storage device of  claim 15 , wherein the processor is further configured to convert the retardation map and the aberration map into one or more lithographic parameters. 
     
     
       20. The non-transitory computer-readable storage device of  claim 19 , wherein the one or more lithographic parameters include at least one of displacement and defocus.